Image reproduction devices like printers, copiers or monitors cannot produce all the colors a human observer can see. In human visual sensation the basic color appearance attributes are hue, lightness and chroma; hue represents the similarity of a color to “one, or a proportion of two, of the perceived colors, red, yellow, green, and blue” (according to a definition by R. W. G. Hunt). Hue is often represented on a color wheel, ranging from red through yellow, green and blue and back to red, with corresponding hue angles, ranging from 0 to 360 degrees.
The term lightness refers to a color's relative position on a scale whose extremes are black (0) and white (100), and chroma values predict the extent to which a color's hue is manifested, ranging from grey (0) to highly chromatic colors on an open-ended scale.
In accordance with these attributes all visible colors can be represented by points in a three-dimensional color space defined by three axes: one achromatic axis (L), representing the lightness values of the colors, and two chromatic axes (a, b), one of them (a) ranging from highly chromatic green through grey to highly chromatic red, the other chromatic axis (b) ranging from highly chromatic blue through grey to highly chromatic yellow. Any possible visible color can be labeled by a unique set of three coordinates (L, a, b), (L) representing its lightness-value and (a) and (b) together representing its hue and chroma whereby (a) and (b) are orthogonal dimensions whose polar equivalents are a hue (an angle) and chroma (a distance from the (a, b) origin).
There are various color models present besides this Lab system such as the HSV (Hue, Saturation, Value) color space, and its variants: HSB (where B stands for Brightness) and HLS (Hue, Lightness, Saturation); more hardware-oriented color representations for instance are systems such as RGB (Red, Green, Blue), used to communicate color signals for monitors or from scanners and digital cameras, CMY (Cyan, Magenta, Yellow) used in printing devices and calorimetrically defined spaces like YIQ (Y for Luminance, I and Q for chromaticity) used in the American TV system and YUV used in the European TV system. The CIE, the Commission International de I'Eclairage established several standards (including CIE XYZ, CIE L*a*b*, CIE LUV and CIECAM02) for specifying color in terms of human perception. The CIE models form the basis for most quantitative color measurements, where CIE L*a*b* is the CIE's variant of the above-mentioned Lab system of coordinates. The discussion herein takes the Lab model and its equivalent polar representation LCH (Lightness, Chroma and Hue) as a basis without being limited to it.
A device's ability to reproduce colors is limited in all its attributes of lightness, chroma and hue; a printer for instance cannot print a yellow more chromatic than the printer's ink, a monitor cannot show a more chromatic red than the red reproduced by the monitor's red phosphor. Similarly, it is not possible to match all the visible colors with a device's limited colorants.
The colors a device can reproduce form a subspace within the color space, called the reproduction device's color gamut. The surface of this subspace, the gamut's boundary, separates the visible though not reproducible out-of-gamut colors from the visible and reproducible in-gamut colors.
One way of defining a gamut's boundary, without being limited to it, is by its extremes in the achievable values of chroma and lightness at all of the color space's hues. For the purposes of computing this boundary, it can be described mathematically. This can be done by using multivariable equations, forming three-dimensional curved hulls. In another approach a finite number of points are derived empirically, these points representing a selection of extreme chroma- and lightness-values, or value that are extreme in terms of other dimensions derived from LCH, a device can reproduce at all of the color space's hues. These points are then used as corner points (vertices) of an interpolated polyhedron surface approximating the reproduction device's boundary.
If an image, or other set of colors, to be reproduced contains colors that are not reproducible by a device, these out-of-gamut colors are replaced by reproducible ones, i.e. out-of-gamut colors are mapped to colors within the reproduction device's gamut. There is a variety of mapping methods, which can be basically categorized by the terms of clipping and compression. Clipping methods specify a mapping criterion, which is used for finding a point on the reproduction device's gamut boundary to which a given out-of-gamut color is mapped; in-gamut colors are kept unchanged. Compression methods are applied to all the colors of an image to be reproduced, thereby changing, in general, all the colors of the image and distributing these changes across the entire range (in some cases, however, even compression methods leave some colors unchanged).
It is also known in the art to combine these basic mapping methods of clipping and compressing. A commonly used combination for instance involves compressing the lightness range of an image to match the lightness range of a reproduction device's gamut prior to the final clipping.
An article by Lindsay MacDonald, Jan Morovic and Kaida Xiao, “A Topographic Gamut Compression Algorithm” (Journal of Imaging Science and Technology, Volume 46, Number 1, January/February 2002) discloses a compression method wherein a core gamut is constructed inside a destination gamut boundary, in which no compression occurs, i.e. color is preserved unchanged. Size and shape of the core gamut is determined by a core white point and a core black point, and a chroma-scaling factor. Colors outside the destination gamut are compressed into the region between the core and the destination gamut using a quadratic function.
U.S. Pat. No. 6,414,690 proposes using local area information to select a most suitable mapping method for a given pixel associated with an out-of-gamut color. One of several mapping methods to select from is described with reference to FIG. 8; a reduced gamut is defined by reducing the chroma of each surface point of the reproduction device's gamut by a predetermined scale factor. Mapping the out-of-gamut colors on the reproduction device's gamut boundary is performed by clipping the out-of-gamut colors onto the reduced-gamut boundary and then using the intersections of the clipping-vectors with the reproduction device's gamut boundary.